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arXiv · 2211.05422

Upper Embeddability of Graphs and Products of Transpositions Associated with Edges

Shuhei Tsujie·Ryo Uchiumi
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Abstract

Given a graph, we associate each edge with the transposition which exchanges the endvertices. Fixing a linear order on the edge set, we obtain a permutation of the vertices. D\'enes proved that the permutation is a full cyclic permutation for any linear order if and only if the graph is a tree. In this article, we characterize graphs having a linear order such that the associated permutation is a full cyclic permutation in terms of graph embeddings. Moreover, we give a counter example for Eden's question about an edge ordering whose associated permutation is the identity.

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Shuhei Tsujie, Ryo Uchiumi. 2022-11-10. Upper Embeddability of Graphs and Products of Transpositions Associated with Edges. https://arxiv.org/abs/2211.05422

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